土木工程外文翻譯--素混凝土的尺寸效應及動態(tài)響應（英文）

1、Size Effects and the Dynamic Response of Plain ConcreteV. Bindiganavile1 and N. Banthia2Abstract: This paper investigates the specimen size effect on the dynamic response of plain concrete. The report is based upon exper

2、imental data by the writers and others and considers results from creep tests on beams, beams under flexural impact, and cylinders under axial impact loading. Size effect is examined using Ba?ant’s size effect law and th

3、e multifractal scaling law, and both scaling models are able to capture the size effect on strength. For fracture energy, on the other hand, the size effect manifests itself only at impact rates. Under quasi-static loadi

4、ng, plain concrete in compression is less sensitive to the specimen size. But under impact, the compressive response appears to be more size dependent than flexure. However, upon accounting for the stress rate effects, t

5、he flexural response depicts a more significant size effect, similar to that seen at quasi-static rates.DOI: 10.1061/?ASCE?0899-1561?2006?18:4?485?CE Database subject headings: Fracture; Concrete; Size effect; Dynamic re

6、sponse.IntroductionThe question of scaling is of a fundamental importance in any physical theory. In a recent article Ba?ant ?1999? presents the history of tackling this issue within solid mechanics. In modern times, the

7、 problem has been consigned to the realm of statistics ever since Weibull proposed his approach ?Weibull 1939? based on the concept of the “weakest link” and the increasing probabil- ity of its occurrence with an increas

8、e in the specimen size. Earlier, Griffith’s energy-based approach to crack propagation ?Griffith 1921? envisaged a size effect, which was material dependent. In the last couple of decades, there have been numerous report

9、s ?Ba?ant 1984; Carpinteri and Chiaia 1997; Karihaloo 1999; Jenq and Shah 1985? about the specimen size effects in quasi-brittle materials. For these materials, Ba?ant states that the source of the size effect is a misma

10、tch between the size dependence of the energy release rate and the rate of energy consumed by fracture ?Ba?ant 2000?. Whereas a significant portion of the former in- creases as the square of the specimen size, the latter

11、 increases linearly. Thus, the reduction in the nominal stress is seen as a means of compensating for this variance by reducing the energy release rate of the specimen. Unlike with quasi-static loading, the study of spec

12、imen size effects in the dynamic domain has not received much attention. Such attempts are confined largely to fiber-reinforced polymers ?Morton 1998; Qian et al. 1990; Liu et al. 1998; Han 1998?. Thedata with respect to

13、 cement-based materials is extremely scarce ?Ba?ant and Gettu 1992; Oh and Chung 1988; Krauthammer et al. 2003; Elfahal et al. 2004; Banthia and Bindiganavile 2002? and attention towards impact rates is very recent. A la

14、ck of design codes or even a standard method for laboratory testing hinders our ability to characterize building materials for constructing impact and blast resistant facilities. Moreover, impact testing in- troduces sev

15、eral extraneous influences such as the inertia ?Banthia et al. 1987? and test machine effects ?Banthia and Bindiganavile 2002?. Perhaps the most serious impediment is the inherent stress- rate sensitivity of cement-based

16、 composites. Morton states that it is not possible to produce an exact scale model for rate-sensitive materials ?Morton 1998?. Further, the suitability of known scaling models under dynamic rates is still under scrutiny.

17、 In this context, a special emphasis must be assigned to explaining the issues of scaling for cement-based materials under high stress rates. In this paper, the size effect on the impact response of concrete is presented

18、 through an assessment of recently published data by the writers and others. Familiar scaling laws developed for quasi- static loading are examined in the context of dynamic stress rates. This paper discusses the interpl

19、ay between the specimen size, matrix strength, stress rate sensitivity, and loading configuration.Scaling Laws for Quasi-Brittle SystemsIt is well known that the quasi-static response of plain concrete is affected by the

20、 size of the specimen. Evidence gathered over decades reveals a strong dependence on size for structural con- crete behavior under compression ?Sabnis and Mirza 1979?, ten- sion ?Ba?ant et al. 1991; van Mier and van Vlie

21、t 2002?, flexure ?Wright 1952; Ba?ant and Li 1995; Jueshi and Hui 1997?, shear ?Ba?ant and Sun 1987?, and torsion ?Zhou et al. 1998?. Three approaches dominate the study of size effects in quasi-brittle ma- terials ?Ba?a

22、nt and Chen 1997?: 1. The statistical theory of random strength; 2. The theory of stress redistribution and fracture energy release caused by large cracks; and 3. The theory of crack fractality. This report focuses on th

23、e two latter models and will examine the size effect in plain concrete under dynamic rates of loading.1Member Technical Staff, U.S. Gypsum Research and Technology Center, 700 N. Highway 45, Libertyville, IL 60048 ?corres

24、ponding author?. E-mail: vivekbs@hotmail.com 2Professor, Dept. of Civil Engineering, Univ. of British Columbia, #2024-6250 Applied Science Lane, CEME Building, Vancouver B.C., V6T 1Z4, Canada. Note. Associate Editor: Zhi

25、shen Wu. Discussion open until January 1, 2007. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The ma

26、nuscript for this paper was submitted for review and possible publication on May 24, 2004; approved on September 23, 2005. This paper is part of the Journal of Materials in Civil Engineering, Vol. 18, No. 4, August 1, 20

27、06. ©ASCE, ISSN 0899- 1561/2006/4-485–491/$25.00.JOURNAL OF MATERIALS IN CIVIL ENGINEERING © ASCE / JULY/AUGUST 2006 / 485Downloaded 05 Mar 2009 to 58.154.176.28. Redistribution subject to ASCE license or copyr

28、ight; see http://pubs.asce.org/copyrightPresent StudyPlain concrete beams of three different sizes were examined under three-point impact. Using a 60 kg hammer, impact tests were conducted at four rates corresponding to

29、incident velocities of 1.98, 3.13, 3.83, and 4.43 m/s. Six specimens were tested for each data point. Dimensions and test conditions for the flexural tests are shown in Fig. 4. The overhang for the three sizes were as fo

30、llows: 150 mm for the 50?50?150 beams, 25 mm for the 100?100?300 beams, and 25 mm for the 150?150?450 beams. ?The length of the overhang was accounted for through Eq. ?4?, where it factors into the inertial correction.?

31、The maxi- mum aggregate size was 10 mm. Quasi-static data was obtained from the study by Chen ?1995?, who examined the beams under four-point loading as per ASTM C 1018 and JSCE SF4. Ba?ant indicated that, in order to st

32、udy specimen size effects ?Ba?ant 1984?, at least three different sizes must be investigated and they must scale in geometric proportion ?e.g., 1:2:4?. How- ever, in the present study, the writers were constrained by the

33、 size of the striking wedge in the impact machine; hence, the beams scale as 1:2:3. Further, for plain concrete beams under impact loading, care must be taken to account for the inertial component of the load as recorded

34、 during the test. Banthia obtained the fol- lowing expression to describe the inertial correction, Pi?t?, for beams under three-point loading ?Banthia 1987?:Pi?t? = ?Au ¨ 0?t?? l3 + 8h33l2? ?4?Thus, the true stressi

35、ng load, Pb?t?, in the impact testing of beams was obtained asPb?t? = Pt?t? ? Pi?t? ?5?where Pt?t?=load as recorded by the hammer.DiscussionStrengthThe results of impact tests in this study as well as those from previous

36、 reports were fitted to Ba?ant’s size effect law ?Eq. ?2?? by means of a mathematical software, employing the Levenberg- Marquardt principle, to arrive at optimized values for d0 and Bft. Similarly, the same data was plo

37、tted according to the multifractal scaling law ?Eq. ?3??, where once again the optimized values for ft and lch were determined by curve-fitting. Fig. 5 shows the data from compression tests on normal strength concrete ?E

38、lfahal et al. 2004? under various stress rates. The data is plotted according toBSEL and implies an increasingly linear elastic response for higher rates of loading. Clearly, there is a size effect for the com- pressive

39、strength, which amplifies with an increase in the rate of loading. In Fig. 6, the same data is described in accordance with MFSL. As with BSEL, here too an increase in the rate of loading leads to a more pronounced size

40、effect. However, according to MFSL, an increase in the impact rate leads to an increase in the characteristic length ?ductility?? of the specimen. Here, it is of interest to note that for low velocities ??10 m/s?, the en

41、ergy required to fracture a beam does increase with an increase in the loading rate. This has been seen not only for plain normal strength concrete but also for high strength concrete, fiber-reinforced con- crete, and co

42、nventionally reinforced concrete ?Banthia 1987?. Figs. 7 and 8 describe the flexural response of plain concrete in accordance with BSEL and MFSL, respectively. Notice once again that, while both models predict an increas

43、e in the size effect with an increase in the stress rate, the size effect is seen to be greater for larger sizes in BSEL, whereas when described by MFSL, the opposite trend emerged. BSEL was postulated prima- rily for no

44、tched specimens. However, from Figs. 5 and 7, it is clear that even for unnotched specimens, the impact response is described well by BSEL. Here, it should be kept in mind that, although four different sizes of cylinders

45、 were examined ?Elfahal et al. 2004?, for some tests, the smallest cylinder ?75?150 mm? yielded results inconsistent with the three larger specimens. TheFig. 4. Dimensions of beams ?square cross section? tested in flexur

46、e in present study ?Note: Quasi-static tests were conducted under four-point loading; actual beam dimensions were 500?150 ?150 mm, 350?100?100 mm, and 450?50?50 mm, resulting in overhang lengths of 25, 25, and 150 mm, re

47、spectively?Fig. 5. Size effect in normal strength cylinders ?Elfahal et al. 2004? as described by BSELFig. 6. Size effect in normal strength cylinders ?Elfahal et al. 2004? as described by MFSLJOURNAL OF MATERIALS IN CIV